Synthetic Turbulence Research Articles

Numerical Analysis of the Impact of the Interior Nozzle Geometry on Low Mach Number Jet Acoustics

The flow and acoustic fields of subsonic turbulent hot jets exhausting from three divergent nozzles at a Mach number M=0.12 based on the nozzle exit velocity are conducted using a hybrid CFD-CAA method. The flow field is computed by highly resolved large-eddy simulations (LES) and the acoustic field is computed by solving the acoustic perturbation equations (APE) whose acoustic source terms are determined by the LES. The LES of the computational domain includes the interior of the nozzle geometry. Synthetic turbulence is prescribed at the inlet of the nozzle to mimic the exit conditions downstream of the last turbine stage. The LES is based on hierarchically refined Cartesian meshes, where the nozzle wall boundaries are resolved by a conservative cut-cell method. The APE solution is determined on a block structured mesh. Three nozzle geometries of increasing complexity are considered, i.e., the flow and acoustic fields of a clean geometry without any built-in components, a nozzle with a centerbody, and a nozzle with a centerbody plus struts are computed. Spectral distributions of the LES based turbulent fluctuated quantities inside the nozzle and further downstream are analyzed in detail. The noise sources in the near field are noticeably influenced by the nozzle built-in components. The centerbody nozzle increases the overall sound pressure level (OASPL) in the near field with respect to the clean nozzle and the centerbody-plus-strut nozzle reduces it compared to the centerbody nozzle due to the increased turbulent mixing. The centerbody perturbed nozzle configurations generate a remarkable spectral peak at S t=0.56 which also occurs in the APE findings in the near field region. This tone is generated by large scale vortical structures shed from the centerbody. The analysis of the individual noise sources shows that the entropy term possesses the highest acoustic contribution in the sideline direction whereas the vortex sound source dominates the downstream acoustics.

A simple extension of digital filter-based turbulent inflow to non-uniform structured grids

The digital filter-based turbulence generator is one of the widely used synthetic turbulence inflow boundary conditions for large-scale-resolving flow simulations. However, the requirement of using uniformly-spaced Cartesian meshes and the limitation of enforcing a constant integral length scale along a given direction restrict the applicability of the method severely. The current paper describes an easy-to-implement and computationally inexpensive approach to extend the digital filter-based inflow to non-uniform structured meshes, using a mapping between the physical curvilinear mesh and a computational uniformly-spaced Cartesian mesh. The method also allows a limited control on the variation of integral length scales over the inflow plane. A zero-pressure-gradient, flat plate turbulent boundary layer is simulated using the proposed method and the distance required by the generated fluctuations to adapt into realistic turbulence is estimated to be about 10 boundary layer thicknesses. The method was developed for and has been used in simulations of turbulent boundary layers along nozzle walls for jet noise applications.

Investigation of turbulence development in incompressible jets with zonal detached eddy simulation (ZDES) and synthetic turbulent inflow

Hybrid RANS/LES simulations of two incompressible jets are performed with the Zonal Detached Eddy Simulation (ZDES). Two functioning modes of the ZDES for the selection of RANS and DES areas are evaluated, namely the user-defined mode (mode 1) and the global- or automatic- mode (mode 2). The RANS-to-LES transition occurs quickly downstream of the nozzle exit and is found to involve the same physics as a laminar to turbulent transition with vortex pairing near the nozzle exit. The effect of the delay in the RANS-to-LES transition on the jet flow development is analyzed. In particular, the delay in the formation of small-scale turbulent structures results in too high turbulence levels in the mixing layers. Furthermore, it is shown, for two cases, that the injection of synthetic turbulence at the nozzle inlet, originally targeted at reproducing the experimental turbulence level in the jet core, has a significant impact on the mixing layer as it accelerates the RANS-to-LES transition, reduces the spatial wavelength of the vortex pairing and promotes the production of fine-scale turbulence which leads to a better agreement with experiments.

Inflow turbulence generation techniques for large eddy simulation of flow and dispersion around a model building in a turbulent atmospheric boundary layer

The present paper investigates the performance of various inflow turbulence generation techniques (ITGT) for large eddy simulation (LES) of flow and dispersion around a model building in a turbulent atmospheric boundary layer. Four different ITGT comprising 1 – no fluctuations, 2 – spectral method, 3 – vortex method and 4 – internal mapping, based on two basic methodologies (i.e. precursor and synthetic turbulence methods), are employed. These techniques are evaluated by considering their prediction accuracy, computational costs, complexity of implementation, inflow information required to operate and impacts on the flow downstream of the inlet, particularly in the wake region of the model building. Results indicate that the accuracy of LES predictions is greatly reliant on ITGT. It is shown that ITGT not only have significant effects on flow field vortical structures, but also influence frequency contents of velocity fluctuations, recirculation regions and plume shapes in the wake region.

Synthetic turbulence: A wavelet based simulation

The treatment of wind-induced vibrations is an important consideration in the design of civil structures with increasing span-lengths and heights. The turbulence in the atmospheric boundary layer has been treated as Gaussian in conventional stochastic simulation schemes, wherein higher-order statistics have been disregarded. However, experimental evidence points at turbulence being a typical multifractal process, which suggests that the statistics at different scales of atmospheric turbulence are not strictly self-similar but exhibit stronger non-Gaussianity as the length scale decreases. Intermittency characterized by the occasional bursts in the wind velocity leads to non-Gaussianity. Intermittency and its potential impact on wind-induced response have been neglected though. Recent studies have addressed the multifractal property of turbulence in wind with wavelet-basis representations of the log-Normal or log-Poisson models. These schemes offer new insight into the simulation of turbulent wind, but suffer from several significant drawbacks, such as the inappropriate sampling of the wavelet coefficients. To overcome these shortcomings, a new simulation scheme, based on the Haar wavelet representation, is proposed in this study where the exact relation between the wind velocities and the wavelet coefficients is introduced. In addition, the effects of intermittency on the wind-induced response of structures are evaluated for a number of cases. A quasi-steady theory-based assessment indicates that the intermittency results in amplifying extremes of the wind-induced response and exhibits higher impact on relatively more rigid structures. It is likely that intermittency may invoke flow-structure interaction with possible enhancement in load effects at related scales, which may further amplify the extremes.

Hybrid Turbulence Model Simulations of Partially Stalled Airfoil Flow

The modified NACA airfoil of the Aeromot 200S Super Ximango motorglider was chosen for wing section simulations at and . A coarse-grid direct numerical simulation was carried out to obtain detailed reference data. A laminar separation bubble close to the leading edge causes transition to turbulence of the suction-side boundary layer. The turbulent boundary layer separates near midchord. The considerable computational expense of this simulation provided the motivation for hybrid simulations based on the model and a one-equation renormalization group model. An extension to the turbulence models that “seeds” synthetic turbulence velocity fluctuations in the parts of the flowfield where the grid resolution changes is proposed but was found to have little effect on the mean flow. When the model contribution was too low, the turbulent boundary layer on the airfoil suction surface separated too early. By increasing the model contribution, a reasonable agreement with the reference data was obtained.

Modelling the effect of freestream turbulence on dynamic stall of wind turbine blades

Large-eddy simulations of flow over a pitching airfoil are conducted to study the effect of freestream turbulence on the aerodynamic characteristics. A primary field of applications of this study is wind turbine aerodynamics. The wind turbines operate in yaw in large scale variations of wind direction due to very large turbulence eddies, and the blades operate in a periodically oscillating condition. The pitching frequency of the airfoil corresponds to a typical rotating frequency of modern large wind turbines. A divergence-free synthetic turbulence inflow is applied at the upstream region of the pitching airfoil to investigate the effect of small-scale freestream turbulence on dynamic stall. Phase-averaged lift, drag and moment of the pitching airfoil show good agreement with experimental data in the literature. Characteristic phenomena of dynamic stall, such as leading edge vortex motions, are analysed and quantified. The effect of the small-scale upstream turbulence is significant on the lift coefficient during the downstroke. The power spectral density of the streamwise velocity sampled from one point in the wake shows that the inertial sub-range tends to extend towards the pitching mode for the turbulent inflow, while there is a distinctive spectral gap for the laminar inflow.

LES study of grid-generated turbulent inflow conditions with moderate number of mesh cells at low Re numbers

ABSTRACTA passive grid-generated turbulence technique for generating turbulent inflow conditions in large-eddy simulation (LES) is developed on moderate number of mesh cells and the results are compared with synthetic methods and wind tunnel experiments performed at Reynolds (Re) number of order 100 (based on Taylor microscale). Consistent with previous investigations, it is found that the synthetic methods turbulence dissipate the turbulence kinetic energy very quickly while the present technique represents this decay more accurately. However, this pre-computation method usually requires considerable computational cost. The aim of this study is, therefore, to decrease the computational cost by employing a relatively coarse mesh resolution accompanied with an appropriate wall modelling approach in the solid boundary. The results are within an acceptable accuracy and, therefore, offer a cost-effective solution to generate inflow turbulence parameters for their use in different aerodynamic applications at low Re numbers.

Assessment of RANS and DES methods for realistic automotive models

This paper presents a comprehensive investigation of RANS and DES models for the Ahmed car body and a realistic automotive vehicle; the DrivAer model. A variety of RANS models, from the 1-equation Spalart Allmaras model to a low-Reynolds number Reynolds Stress model have shown an inability to consistently correctly capture the flow field for both the Ahmed car body and DrivAer model, with the under-prediction of the turbulence in the initial separated shear layer found as a key deficiency. It has been shown that the use of a hybrid RANS-LES model (in this case, Detached Eddy Simulation) offers an advantage over RANS models in terms of the force coefficients, and general flow field for both the Ahmed car body and the DrivAer model. However, for both cases even at the finest mesh level hybrid RANS-LES methods still exhibited inaccuracies. Suggestions are made on possible improvements, in particular on the use of embedded LES with synthetic turbulence generation. Finally the computational cost of each approach is compared, which shows that whilst hybrid RANS-LES offer a clear benefit over RANS models for automotive relevant flows they do so at a much increased cost.

Experimental Investigation and Large-Eddy Simulation of the Turbulent Flow past a Smooth and Rigid Hemisphere

The objective of the present paper is to provide a detailed experimental and numerical investigation on the turbulent flow past a hemispherical obstacle (diameter D). For this purpose, the bluff body is exposed to a thick turbulent boundary layer of the thickness δ = D/2 at Re = 50,000. In the experiment this boundary layer thickness is achieved by specific fences placed in the upstream region of the wind tunnel. A detailed measurement of the upstream flow conditions by laser-Doppler and hot-film probes allows to mimic the inflow conditions for the complementary large-eddy simulation of the flow field using a synthetic turbulence inflow generator. These clearly defined boundary and operating conditions are the prerequisites for a combined experimental and numerical investigation of the flow field relying on the laser-Doppler anemometry and a finite-volume Navier-Stokes solver for block-structured curvilinear grids. The results comprise an analysis on the unsteady flow features observed in the vicinity of the hemisphere as well as a detailed discussion of the time-averaged flow field. The latter includes the mean velocity field as well as the Reynolds stresses. Owing to the proper description of the oncoming flow and supplementary numerical studies guaranteeing the choice of an appropriate grid and subgrid-scale model, the results of the measurements and the prediction are found to be in close agreement.

Large eddy simulation studies on the influence of turbulent inlet conditions on the flow behavior in a mixing tee

Mixing of coolant streams at significant temperature differences in a mixing tee occurs in the cooling systems (e.g. Residual Heat Removal System) of a nuclear power plant resulting in cyclical thermal fluctuations that may lead to high cycle thermal fatigue (HCTF) in the structure. The present study aims to numerically investigate such a scenario using the large-eddy simulation (LES) method. The LES is based on an experiment conducted at the fluid–structure interaction (FSI) test facility, University of Stuttgart. Hot and cold water streams flow in the main and branch pipes with a temperature difference (ΔT) of 117K. The mass flow rate ratio (main/branch) is 4:1.Two LESs with different inlet conditions are performed to study and compare the effect of each inlet condition on the flow behavior downstream of the mixing tee. They are (i) unperturbed inlet conditions and (ii) inlets with synthetic turbulence. The experimental inflow conditions result in an incompletely mixed thermally stratified flow marked by significant buoyancy effects. Assessment of parameters like mean temperature and velocity predicted by both LESs exhibit very little deviation with each other indicating the insignificant effect of inflow turbulence on the bulk flow. But the inclusion of inflow turbulence is seen to have a non-negligible effect in the assessment of parameters like temperature fluctuations, turbulent kinetic energy and temperature–velocity correlation. The prevailing flow conditions are not seen to induce any dominant frequency of near-wall temperature fluctuations, an important factor in thermal fatigue analysis. Energy content of these fluctuations mainly lies in the frequency range of 0.1–2Hz.

Numerical Predictions of Turbulence/Cascade-Interaction Noise Using Computational Aeroacoustics with a Stochastic Model

Turbulent-flow interactions with the outlet guide vanes are known to mainly contribute to broadband-noise emission of aeroengines at approach conditions. This paper presents a three-dimensional computational aeroacoustics hybrid method aiming at simulating the aeroacoustic response of an annular cascade impacted by a prescribed homogeneous isotropic turbulent flow. It is based on a time-domain Euler solver coupled to a synthetic turbulence model implemented in the code by means of a suited inflow boundary condition. The fluctuating pressure over the airfoil surface provided by computational aeroacoustics is used as an input to a Ffowcs Williams and Hawkings integral method to calculate the radiated sound field. Euler computations are first validated against an academic computational aeroacoustics benchmark in the case of an harmonic gust interacting with an annular flat-plate cascade. Then, simulations are applied to turbulence–cascade interactions for annular configurations, in uniform and swirling mean flows, and numerical results in terms of sound power spectra in the outlet duct are compared to semi-analytical and numerical solutions, and to an available experiment.

Zonal RANS–LES approach based on an algebraic reynolds stress model

The zonal RANS–LES approach based on the algebraic EARSM Reynolds stress model is considered. Using the EARSM model makes it possible to increase the accuracy of modeling the turbulent parameters at the RANS–LES interface in the case of flows in asymmetric designs and near dihedrals. This favors the more accurate modeling of vortex structures by the synthetic turbulence generator and, as a consequence, the narrowing of the transition zone behind the RANS–LES interface. The application of this approach is analyzed with reference to the examples of flows in a square channel and an asymmetric diffuser.

Extended Synthetic Turbulence Inflow Generator within a Hybrid LES–URANS Methodology for the Prediction of Non–Equilibrium Wall–Bounded Flows

The objective of the present paper is the fusion of a proper synthetic turbulence inflow generator with an unified hybrid LES–URANS method. The hybrid approach relies on an explicit algebraic Reynolds stress model within the unsteady Reynolds–averaged Navier–Stoks (URANS) mode. To extend the application area of the hybrid method, the digital filter concept by Klein et al. (J. Comp. Phys. 186, 652–665, 2003) is employed. Due to the application of the inflow generator within the hybrid simulation, an additional formulation for the modeled turbulent kinetic energy is necessary to ensure a reasonable inflow profile for this quantity. The required integral time scale and the two integral length scales are presently determined based on pre–simulations applying periodic boundary conditions but can also rely on other sources such as experimental data. With the aid of these integral scales and reference profiles of the mean velocity and the Reynolds stress tensor instantaneous inflow velocity profiles are generated. The integral scales are evaluated for the plane channel flow (Re t = 590) as well as the periodic hill flow (Re b = 10,595). The generated inflow data are used for these test cases and extensively evaluated. Besides the analysis of the adaptation length for both benchmarks, the mean profiles of the velocity as well as selected second–order moments of the simulations applying the synthetic inflow profiles are compared with reference data and results of hybrid simulations applying periodic boundary conditions. Furthermore, the influence of the grid resolution is analyzed.

The evolution towards the rod-like axisymmetric structure for turbulent stress tensor

Modelling the turbulent stress tensor is a main task for both large eddy simulations and methods based on Reynolds averaged Navier-Stokes equations. The turbulent stress is known as the subgrid-scale stress in the former and the Reynolds stress in the latter. In this paper, we examine the observation that the stress tensor tends to evolve towards a rod-like axisymmetric configuration. This observation has been well documented for the subgrid-scale stress. However, for the Reynolds stress, the available data are still too limited to draw a definite conclusion. In the first part of the paper, we show that the tendency is also universal for the Reynolds stress by direct numerical simulations of decaying anisotropic turbulence. To show the universality, it is crucial to examine the decaying process from initial turbulent fields with a wide range of levels of anisotropy. Such initial fields are generated by a novel synthetic turbulence model based on the so-called constrained multi-turnover Lagrangian map. In the second part, we use the direct numerical simulation data to study the dynamical mechanisms of the evolution towards the rod-like structures. Among others, the analyses show that the nonlinear self-interaction term is the driving force of the process, and that the pressure tends to enhance the disk-like axisymmetric structure but overall tends to reduce the anisotropy of the stress tensor. The results shed light on the subtle difference between the pressure and the nonlinear self-interaction terms.

Wake downstream of the Lillgrund wind farm - A Comparison between LES using the actuator disc method and a Wind farm Parametrization in WRF

Simulations of the Lillgrund wind farm (located between Malmo and Copenhagen) are performed using both Large Eddy Simulation (LES) and mesoscale simulations in WRF. The aim is to obtain a better understanding of wakes generated by entire wind farms in order to improve the understanding of farm to farm interactions. The study compares the results from the two used models for the energy production and the wake characteristics downstream of the wind farm. A comparison is also performed with regards to the production data from the Lillgrund wind farm which has been filtered to be comparable to the case used in the simulations.The studied case, based on a prerun in WRF without any wind farm, has an inflow angle of 222 ± 2.5 deg, a wind speed at hub height of 9.8 m/s and a near neutral atmosphere. A logarithmic wind shear is used in LES and the turbulence intensity is 5.9%.The WRF simulations use a parameterization for wind farms. The wind farm is treated by the model as a sink of the resolved atmospheric momentum. The total energy extraction and the electrical power are respectively proportional to specified thrust and power coefficients. The generated turbulent kinetic energy arethe difference between the total and the electrical power.The LES are performed using the EllipSys3D code applying the actuator disc methodology for representing the presence of the rotors. Synthetic atmospheric turbulence is generated with the Mann model. Both the atmospheric turbulence and the wind shear are introduced using body forces.The production was found to be better estimated in LES. WRF show a slightly higher recovery behind the farm. The internal boundary layer is for the compared simulation setups higher in LES while the wake expansion is about the same in both models. The results from the WRF parameterization could potentially be improved by increasing the grid resolution. For farm to farm interaction a combination of the two methods is found to be of interest.

Inflow turbulence generation methods with large eddy simulation for wind effects on tall buildings

Generation of turbulent inflow conditions matching realistic wind flow characteristics in atmospheric boundary layer (ABL) is essential for accurate predictions of wind effects on buildings and structures using large eddy simulation (LES). It is thus necessary to evaluate the performances of different inflow turbulence generation techniques. In this study, four inflow turbulence generation methods (including three synthetic turbulence methods and the recycling method) were used to simulate wind flows in ABL for LES of wind loadings on a tall building. The advantages and limitations of these inflow turbulence generation methods were discussed through comparisons with available wind tunnel measurements and previous numerical simulation results. Several remedial measures were presented to improve the performances of these inflow turbulence generation methods. The findings of this paper are of use and interest to researchers and designers involved in the wind-resistant design of tall buildings, since one can follow the established procedure to predict the dynamic wind loadings on tall buildings by LES.

A stochastic perturbation method to generate inflow turbulence in large-eddy simulation models: Application to neutrally stratified atmospheric boundary layers

Despite the variety of existing methods, efficient generation of turbulent inflow conditions for large-eddy simulation (LES) models remains a challenging and active research area. Herein, we extend our previous research on the cell perturbation method, which uses a novel stochastic approach based upon finite amplitude perturbations of the potential temperature field applied within a region near the inflow boundaries of the LES domain [Muñoz-Esparza et al., “Bridging the transition from mesoscale to microscale turbulence in numerical weather prediction models,” Boundary-Layer Meteorol., 153, 409–440 (2014)]. The objective was twofold: (i) to identify the governing parameters of the method and their optimum values and (ii) to generalize the results over a broad range of atmospheric large-scale forcing conditions, Ug = 5 − 25 m s−1, where Ug is the geostrophic wind. We identified the perturbation Eckert number, Ec=Ug2/ρcpθ̃pm, to be the parameter governing the flow transition to turbulence in neutrally stratified boundary layers. Here, θ̃pm is the maximum perturbation amplitude applied, cp is the specific heat capacity at constant pressure, and ρ is the density. The optimal Eckert number was found for nonlinear perturbations allowed by Ec ≈ 0.16, which instigate formation of hairpin-like vortices that most rapidly transition to a developed turbulent state. Larger Ec numbers (linear small-amplitude perturbations) result in streaky structures requiring larger fetches to reach the quasi-equilibrium solution, while smaller Ec numbers lead to buoyancy dominated perturbations exhibiting difficulties for hairpin-like vortices to emerge. Cell perturbations with wavelengths within the inertial range of three-dimensional turbulence achieved identical quasi-equilibrium values of resolved turbulent kinetic energy, q, and Reynolds-shear stress, 〈w′u′〉. In contrast, large-scale perturbations acting at the production range exhibited reduced levels of 〈w′u′〉, due to the formation of coherent streamwise structures, while q was maintained, requiring larger fetches for the turbulent solution to stabilize. Additionally, the cell perturbation method was compared to a synthetic turbulence generator. The proposed stochastic approach provided at least the same efficiency in developing realistic turbulence, while accelerating the formation of large-scales associated with production of turbulent kinetic energy. Also, it is computationally inexpensive and does not require any turbulent information.

Anisotropic linear forcing for synthetic turbulence generation in large eddy simulation and hybrid RANS/LES modeling

A general forcing method for Large Eddy Simulation (LES) is proposed for the purpose of providing the flow with fluctuations that satisfy a desired statistical state. This method, the Anisotropic Linear Forcing (ALF) introduces an unsteady linear tensor function of the resolved velocity which acts as a restoring force in the mean velocity and resolved stress budgets. The ALF generalizes and extends several forcing previously proposed in the literature. In order to make it possible to impose the integral length scale of the turbulence generated by the forcing term, an alternative formulation of the ALF, using a differential spatial filter, is proposed and analyzed. The anisotropic forcing of the Reynolds stresses is particularly attractive, since unsteady turbulent fluctuations can be locally enhanced or damped, depending on the target stresses. As such, it is shown that the ALF is an effective method to promote turbulent fluctuations downstream of the LES inlet or at the interface between RANS and LES in zonal hybrid RANS/LES modeling. The detailed analysis of the influence of the ALF parameters in spatially developing channel flows and hybrid computations where the ALF target statistics are given by a RANS second-moment closure show that this original approach performs as well as the synthetic eddy method. However, since the ALF method is more flexible and significant computational savings are obtained, the method appears a promising all-in-one solution for general embedded LES simulations.

Correlation between the phase and the log-amplitude of a wave through vertical atmospheric propagation

Expressions of the correlation between the log-amplitude and the phase of a wavefront propagating through atmospheric turbulence are presented. These expressions are useful to evaluate the feasibility of proposed methods to increase the confidence level of the detection of faint transient astronomical objects. The properties of the derived angular correlation functions are discussed using usual synthetic turbulence profiles. The close formulation between the phase and the log-amplitude allows an analytic formulation in the Rytov approximation. Equations contain the product of an arbitrary number of hypergeometric functions that are evaluated using the Mellin transforms integration method.